1. Field of the Invention
The invention relates generally to the analysis of under ground earth formations, and, more particularly, to the determination of formation resistivity and hydrocarbon saturation.
2. Background Art
The localization and quantification of low resistivity pay (sometimes known as low contrast pay) is a primary goal of oil and gas exploration. Hydrocarbon saturations or bulk hydrocarbon volume (BVH) in subsurface isotropic and homogeneous rocks are usually estimated through the use of Archie type equations, which relate the porosity and water saturation in the pore space of the rock to the resistivity of the rock. For example, BVH in a formation may be determined from the total porosity (φT) and the total water saturation (Swt) of the formation according to the relationship: BVH=φT(1−Swt). While the total porosity (φT) may be determined with various tools (e.g., NMR, neutron, density, sonic etc.), the total water saturation (Swt) often is derived from resistivity and porosity measurements, using the Archie equation or its variants (generally referred to as “Archie equations”). This approach of deriving Swt from resistivity and porosity measurements usually works satisfactorily once the parameters of the equations are fine tuned with measurements or tests performed in the area. However, this approach of using Archie equations to derive Swt breaks down with relation to anisotropic formations, and new methods are needed in this situation.
Formation resistivity can be measured with conventional logging instruments equipped with electrodes (laterologs) or antennas that can transmit a current or electromagnetic (EM) energy into earth formations (induction/propagation logs). The instruments are disposed within a borehole traversing the formations and energy is transmitted into the formations to interact with the conductive media in the formations. With laterologs, a current (or voltage) is injected (or applied) into a formation using a first pair of electrodes and a second pair of electrodes are typically placed at a distance from the first pair of electrodes to measure the voltage drop or current flow between the second pair of electrodes. The measured voltage drop or current flow may then be used to derive the resistivity (or its inverse, conductivity) of the formation.
With induction/propagation logging, EM energy is transmitted into a formation to induce eddy currents in the formation. The eddy currents flow in loops that lie in planes perpendicular to the magnetic dipole of the transmitting antenna. The magnitudes of the eddy currents depend on the conductivities of the formation. The eddy currents in turn induce secondary magnetic fields, the magnitudes of which depend on the magnitudes of the eddy currents. Therefore, by measuring the magnitudes of the secondary magnetic fields (using a receiver antenna), it is possible to indirectly determine the resistivity of the formation around the transmitter and receiver antennas.
Resistivities of earth formations depend on the amounts and types of fluids included in the pores therein. Thus, different formations may have different resistivities due to different porosities, and/or different amounts or types of fluids included therein. When the formation is isotropic and homogeneous, its electric properties are constant regardless of the direction of the measurements. However, earth formations often comprise geological (sedimentation) layers that may have different petrophysical properties (e.g., porosities, saturations, grain sizes etc.), and hence electrical properties. Consequently, resistivity measurements may produce different results when measured in different directions. This phenomenon is referred to as formation (electrical) anisotropy.
In a typical situation, a borehole may be drilled through multiple sedimentation layers in a direction perpendicular to the layers, i.e., a vertical well with no formation dip. In such a vertical well, a resistivity measurement along a direction parallel the borehole axis is referred to as a vertical resistivity (Rv) because the measurement is made in a direction perpendicular to the sedimentation layers. In the vertical resistivity measurements, the current paths run through various sedimentation layers, which act like different resistors connected in series. Therefore, the apparent resistivity of the formation (Rv) is a summation of resistivities contributed by individual layers. For example, as described below by the present invention, in a two-electrical-layer model comprising a relative-ower-resistivity layer and a relative-higher-resistivity layer finely interlaced together,Rv=RlrVFlr+RhrVFhr,  (1)where Rv is the measured (apparent) vertical resistivity, VFlr and Rlr are the volume fraction and resistivity of the relative-lower-resistivity layer, and VFhr and Rhr are the volume fraction and resistivity of the relative-higher-resistivity layer. As seen from Equation (1), the vertical resistivity measurements (Rv) would be dominated by more resistive layers (e.g., hydrocarbon-bearing layers). In contrast, highly conductive thin layers (e.g., brine-bearing layers) may be obscured by the more resistive layers in such measurements.
In contrast, if a resistivity measurement is performed along a direction perpendicular to the borehole axis (or equivalently parallel to the beddings) in such a vertical well, it is referred to as horizontal resistivity (Rh) because the measurement is made along the sedimentation planes. Note that the “horizontal” and “vertical” used herein are with respect to the sedimentation layers, rather than with respect to the borehole axis. In horizontal resistivity measurements in a vertical well, currents flow in planes perpendicular to the borehole axis, i.e., within sedimentation layers. Thus, each individual sedimentation layer provides a conductive path for the currents, i.e., the sedimentation layers form parallel circuits. As a result, the measured conductance (1/Rh) is a summation of the conductivities of the sedimentation layers within the region of investigation. For example, in the electrical-layered model comprising relative-lower-resistivity and relative-higher-resistivity layers,                               1                      R            h                          =                                            VF              lr                                      R              lr                                +                                    VF              hr                                      R              hr                                                          (        2        )            where Rh is the horizontal resistivity, VFlr and Rlr represent the volume fraction and resistivity of the relative-lower-resistivity layer, and VFhr and Rhr represent the volume fraction and resistivity of the relative-higher-resistivity layer, respectively. As seen from Equation (2), the measured horizontal conductivity (Rh) would be dominated by the most conductive layers, while thin non-conductive hydrocarbon-bearing layers may become “invisible” to the horizontal resistivity measurements. This is known as the low resistivity pay problem.
As mentioned above, either the conductive layers or the resistive layers could be “missed” in the resistivity measurements depending on the direction of the measure ments, in the sense that their presence has only a small effect on the apparent resistivity. Thus, formation resistivity anisotropy presents a problem in formation evaluation. Many reservoir rocks exhibit resistivity anisotropy. Several mechanisms can produce the anisotropy, among which are very thin sand (carbonate)-shale laminations, grain size changes in clean sandstone, wind-distributed sands (aeolian formations), cementing (porosity) changes in sandstone and so on. See Rubin, D. M., Cross bedding, bed-forms, and paleocurrents, Society Of Economic Paleontologists And Mineralogists, Concepts In Sedimentology And Paleontology, 1; Klein et al., The petrophysics of electrically anisotropic reservoirs, Transactions of the SPWLA Thirty-Sixth Annual Logging Symposium, Paris, France, Jun. 26–29, 1995, paper HH.
Over the years, most of the homogeneous or thick-layer oil and gas reservoirs have been discovered. As a result, many reservoirs comprise thin layers of pay zones. With technology advances such as directional and horizontal drilling, it is becoming economical to produce in thin reservoirs that traditionally would have been ignored. The industry has also begun to realize the importance of thinly laminated reservoirs that have been by-passed due to low apparent resistivity in vertical wells. Therefore, a need ex ists for methods that can accurately predict the hydrocarbon contents of thinly laminated reservoirs.
Evaluation of thinly laminated reservoirs is not a new problem in formation evaluation and interpretation. See U.S. Pat. Nos. 3,166,709 and 5,461,562, assigned to the present assignee. The horizontal and vertical resistivities of anisotropic formations can be evaluated by wireline or logging-while-drilling (LWD) EM measurements in highly deviated wells. See Hagiwara T., A New Method to Determine Horizontal-Resistivity in Anisotropic Formations with Prior Knowledge of Relative Dip, Transactions of the SPWLA Thirty-Seventh Annual Logging Symposium, Jun. 16–19, 1996, Paper Q; U.S. Pat. Nos. 5,966,013, 6,092,024, 5,886,526, 6,218,841. Recent techniques using tri-axial EM tools and the combination of EM tools with laterolog tools have made it possible to measure the vertical and horizontal resistivities in vertical wells. However, it remains a difficult task to relate the measured resistivities (Rv and Rh) to the bulk hydrocarbon volume because the traditional Archie relation does not apply to anisotropic formations.
Several papers have been published dealing with analyses of anisotropic formations. See Klein et al., The Petrophysics of Electronically Anisotropic Reservoirs, Transactions of the SP-WLA Thirty-Sixth Annual Logging Symposium, Jun. 26–29, 1995, Paper HH; Tabanou et al., Which Resistivity Should Be Used To Evaluate Thinly Bedded Reservoirs at High Angle? Transactions of the SPWLA Fortieth Annual Logging Symposium, May 30–Jun. 3, 1999, Paper E; Shray F. and Borbas T., Evaluation of Laminated Formations Using Nuclear Resonance and Resistivity Anisotropy Measurements, SPE Eastern Regional Meeting, Canton, Ohio 17–19 October 2001; U.S. Pat. No. 5,550,473.
These papers propose methods for determining electrical properties of anisotropic formations. As shown in Equations (1) and (2), four parameters (VFhr, Rhr, VFlr, and Rlr) are determined in order to define the electrical properties of a two-layer model. WithVFhr+VFlr=1,  (3)there are four unknowns and three equations. Note that Rh and Rv are assumed known parameters that can be deter mined from resistivity measurements. Thus, one additional parameter is needed to solve these equations.
Depending on the additional parameter that is used to solve these equations (hence, electrical properties of the formation layers), conventional methods may be categorized as theRv-Rh-φr-Rsh method, theRv-Rh-φr-Vsh method, and theRv-Rh-φT-BFVmethod, where Rsh, Vsh and BFV are shale resistivity, shale content, and bound fluid volume, respectively. Once the electrical properties of the formation layers (e.g., Rhr and Rlr) are known, they can be used together with the total porosity (φT) of the formation to determine the total water saturation (Swt). The total water saturation (Swt) and total porosity (φT) may then be used to determine the bulk hydrocarbon volume (BVH) according to the relationship BVH=φT(1−Swt). It is assumed that a reliable technique exists for the water saturation evaluation of each of the individual homogeneous layers in the layered model. The Archie relation is typically assumed applicable in the individual layers.
The additional parameter used in these methods is either obtained from other types of measurements (e.g., NMR, GR) or assumed to be the same as the value determined in a thick layer of the same composition. However, these assumed values may not accurately represent the values of the same types of layers in thin laminations. In addition, these methods are based on assumptions of formation geological compositions and petrophysical properties (i.e., grain sizes or porosities). If the formation has a different composition or property from that assumed, these methods cannot provide accurate estimates of electrical properties of the formation layers. As a result, the derived Swt and BVH may not be accurate.
Thus a need remains for improved techniques that can provide accurate Swt and BVH estimates without prior knowledge of the properties of the thin layers of the formation.